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Number Systems - Practice MCQs for CCAT

50 Questions Section B: Programming Computer Fundamentals

Number Systems Question Bank for C-CAT

Practice 50 Number Systems multiple-choice questions designed for CDAC CCAT exam preparation. Questions are paginated in sets of 10 and include detailed explanations.

50 total MCQs 10 per page Detailed explanations
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What this topic covers

  • Topic-wise Number Systems MCQs for C-CAT preparation.
  • Detailed explanations after every answer.
  • Focused revision questions for stronger preparation.
Q1.
Binary number system has base:
A16
B8
C10
D2
Show Answer & Explanation

Correct Answer: D - 2

Binary is base-2 number system using only 0 and 1.

Q2.
Hexadecimal number system has base:
A16
B8
C10
D2
Show Answer & Explanation

Correct Answer: A - 16

Hexadecimal is base-16, using digits 0-9 and letters A-F.

Q3.
Convert (10)_10 to binary:
A1010
B1000
C1100
D1110
Show Answer & Explanation

Correct Answer: A - 1010

10 in decimal = 1010 in binary (8+2=10).

Q4.
Convert (1101)_2 to decimal:
A11
B13
C12
D14
Show Answer & Explanation

Correct Answer: B - 13

1101_2 = 8+4+0+1 = 13 in decimal.

Q5.
(F)_16 equals in decimal:
A14
B17
C16
D15
Show Answer & Explanation

Correct Answer: D - 15

F in hexadecimal = 15 in decimal.

Q6.
(17)_8 in decimal is:
A13
B14
C16
D15
Show Answer & Explanation

Correct Answer: D - 15

17_8 = 1×8 + 7×1 = 8+7 = 15 in decimal.

Q7.
Octal number system has base:
A2
B16
C10
D8
Show Answer & Explanation

Correct Answer: D - 8

Octal is base-8 number system using digits 0-7.

Q8.
1's complement of 1010 is:
A1001
B1010
C0110
D0101
Show Answer & Explanation

Correct Answer: D - 0101

1's complement is obtained by inverting all bits: 1010 -> 0101.

Q9.
2's complement of 1010 is:
A0101
B0110
C1001
D1011
Show Answer & Explanation

Correct Answer: B - 0110

2's complement = 1's complement + 1 = 0101 + 1 = 0110.

Q10.
(10)_16 in decimal is:
A10
B15
C16
D8
Show Answer & Explanation

Correct Answer: C - 16

10_16 = 1×16 + 0×1 = 16 in decimal.

Q11.
What is the binary equivalent of the decimal number 25?
A10101
B10011
C11001
D11010
Show Answer & Explanation

Correct Answer: C - 11001

25 in decimal = 16+8+1 = 11001 in binary.

Q12.
What is the decimal equivalent of the binary number 1101?
A11
B12
C13
D14
Show Answer & Explanation

Correct Answer: C - 13

1101 in binary = 1×8 + 1×4 + 0×2 + 1×1 = 13 in decimal.

Q13.
What is the hexadecimal equivalent of the decimal number 255?
AEF
BFE
CFF
DF0
Show Answer & Explanation

Correct Answer: C - FF

255 = 15×16 + 15 = FF in hexadecimal.

Q14.
What is the octal equivalent of binary number 110101?
A63
B53
C65
D55
Show Answer & Explanation

Correct Answer: C - 65

Group binary from right: 110 101 = 6 5, so the octal equivalent is 65.

Q15.
What is the result of binary addition: 1011 + 1101?
A11000
B10100
C11010
D10110
Show Answer & Explanation

Correct Answer: A - 11000

1011 (11) + 1101 (13) = 11000 (24) in binary.

Q16.
The base of the hexadecimal number system is:
A2
B16
C10
D8
Show Answer & Explanation

Correct Answer: B - 16

The hexadecimal number system has a base (radix) of 16, using digits 0-9 and letters A-F.

Q17.
What is the 1's complement of the binary number 1010?
A0110
B1010
C0101
D1001
Show Answer & Explanation

Correct Answer: C - 0101

The 1's complement is obtained by flipping each bit: 1010 becomes 0101.

Q18.
What is the 2's complement of the binary number 1100?
A0011
B1101
C0101
D0100
Show Answer & Explanation

Correct Answer: D - 0100

2's complement = 1's complement + 1. 1's complement of 1100 = 0011; 0011 + 1 = 0100.

Q19.
Convert hexadecimal 2A to decimal:
A40
B46
C44
D42
Show Answer & Explanation

Correct Answer: D - 42

2A hex = 2×16 + 10×1 = 32 + 10 = 42 in decimal.

Q20.
What is the binary equivalent of octal number 37?
A011111
B011011
C110111
D101111
Show Answer & Explanation

Correct Answer: A - 011111

Convert each octal digit to 3-bit binary: 3 = 011, 7 = 111. So 37 octal = 011111 binary.

Q21.
In which number system is the digit 'A' valid?
AHexadecimal
BOctal
CDecimal
DBinary
Show Answer & Explanation

Correct Answer: A - Hexadecimal

In hexadecimal, letters A-F represent values 10-15, making 'A' a valid digit.

Q22.
What is the result of binary subtraction: 1010 - 0011?
A0110
B1001
C1000
D0111
Show Answer & Explanation

Correct Answer: D - 0111

1010 (10) - 0011 (3) = 0111 (7) in binary.

Q23.
What is the decimal equivalent of hexadecimal number 1F?
A25
B27
C31
D33
Show Answer & Explanation

Correct Answer: C - 31

1F hex = 1×16 + 15×1 = 16 + 15 = 31 in decimal.

Q24.
How many unique symbols does the octal number system use?
A2
B8
C10
D16
Show Answer & Explanation

Correct Answer: B - 8

The octal number system uses 8 unique symbols: 0, 1, 2, 3, 4, 5, 6, and 7.

Q25.
What is (110)₂ × (11)₂ in binary?
A1010
B10010
C1110
D10000
Show Answer & Explanation

Correct Answer: B - 10010

110 (6) × 11 (3) = 10010 (18) in binary.

Q26.
Convert decimal 100 to binary:
A1100010
B1100100
C1010100
D1001100
Show Answer & Explanation

Correct Answer: B - 1100100

100 = 64+32+4 = 1100100 in binary.

Q27.
What is the decimal equivalent of octal number 72?
A58
B56
C54
D60
Show Answer & Explanation

Correct Answer: A - 58

72 octal = 7×8 + 2×1 = 56 + 2 = 58 in decimal.

Q28.
The highest digit in an octal number system is:
A7
B6
C8
D9
Show Answer & Explanation

Correct Answer: A - 7

The octal system uses digits 0-7, so 7 is the highest valid digit.

Q29.
What is the hexadecimal equivalent of binary 11110000?
AE0
BF0
CEF
D0F
Show Answer & Explanation

Correct Answer: B - F0

Group binary into 4 bits: 1111 = F, 0000 = 0. So 11110000 binary = F0 hex.

Q30.
What is the 2's complement representation of -5 in 8-bit binary?
A11111010
B10000101
C11111011
D10000100
Show Answer & Explanation

Correct Answer: C - 11111011

5 = 00000101. 1's complement = 11111010. 2's complement = 11111010 + 1 = 11111011.

Q31.
Convert binary 1010.11 to decimal:
A10.5
B11.75
C10.25
D10.75
Show Answer & Explanation

Correct Answer: D - 10.75

1010 = 10. After the point: 1×0.5 + 1×0.25 = 0.75. Total = 10.75.

Q32.
What is the BCD (Binary Coded Decimal) representation of decimal 9?
A1001
B1010
C1011
D1000
Show Answer & Explanation

Correct Answer: A - 1001

In BCD, each decimal digit is represented by its 4-bit binary equivalent. 9 = 1001.

Q33.
Which of the following is NOT a valid octal number?
A567
B789
C123
D345
Show Answer & Explanation

Correct Answer: B - 789

789 is not valid in octal because digits 8 and 9 are not part of the octal system (0-7).

Q34.
What is the result of the hexadecimal addition: A + 7?
A10
B17
C11
DF
Show Answer & Explanation

Correct Answer: C - 11

A (10) + 7 = 17 in decimal. 17 = 1×16 + 1 = 11 in hexadecimal.

Q35.
Convert decimal 200 to hexadecimal:
AC0
BD0
CC8
DD8
Show Answer & Explanation

Correct Answer: C - C8

200 ÷ 16 = 12 remainder 8. So 200 decimal = C8 hexadecimal.

Q36.
In the 2's complement system, the MSB (Most Significant Bit) represents:
ASign
BParity
COverflow
DMagnitude
Show Answer & Explanation

Correct Answer: A - Sign

In 2's complement representation, the MSB is the sign bit: 0 for positive, 1 for negative.

Q37.
What is the Gray code equivalent of binary 1011?
A1010
B1101
C1100
D1110
Show Answer & Explanation

Correct Answer: D - 1110

Gray code: MSB stays same (1). Then XOR adjacent bits: 1⊕0=1, 0⊕1=1, 1⊕1=0. Result: 1110.

Q38.
Convert octal 15 to hexadecimal:
AB
BC
CD
DE
Show Answer & Explanation

Correct Answer: C - D

Octal 15 = 1×8 + 5 = 13 decimal = D hexadecimal.

Q39.
What is the range of values that can be represented by an 8-bit unsigned binary number?
A0 to 127
B0 to 255
C-128 to 127
D1 to 256
Show Answer & Explanation

Correct Answer: B - 0 to 255

An 8-bit unsigned binary number can represent values from 0 (00000000) to 255 (11111111).

Q40.
What is the excess-3 code for decimal digit 4?
A0111
B0100
C1000
D0011
Show Answer & Explanation

Correct Answer: A - 0111

Excess-3 code adds 3 to the decimal digit before converting to binary: 4 + 3 = 7 = 0111.

Q41.
What is the binary equivalent of hexadecimal number B3?
A10100011
B10110011
C11000011
D10110001
Show Answer & Explanation

Correct Answer: B - 10110011

B = 1011, 3 = 0011. So B3 hex = 10110011 binary.

Q42.
What is the decimal equivalent of BCD number 0100 0111?
A47
B45
C43
D74
Show Answer & Explanation

Correct Answer: A - 47

BCD 0100 = 4, 0111 = 7. So the decimal equivalent is 47.

Q43.
Perform binary division: 1100 ÷ 10:
A101
B110
C100
D111
Show Answer & Explanation

Correct Answer: B - 110

1100 (12) ÷ 10 (2) = 110 (6) in binary.

Q44.
What is the signed magnitude representation of -7 in 8-bit binary?
A10000110
B11111001
C11111000
D10000111
Show Answer & Explanation

Correct Answer: D - 10000111

In signed magnitude, the MSB is 1 for negative. 7 = 0000111. So -7 = 10000111.

Q45.
Convert hexadecimal FF to octal:
A375
B377
C367
D357
Show Answer & Explanation

Correct Answer: B - 377

FF hex = 255 decimal. 255 ÷ 8 = 31 remainder 7; 31 ÷ 8 = 3 remainder 7; 3 ÷ 8 = 0 remainder 3. So 255 = 377 octal.

Q46.
What is the result of adding 1 to the binary number 1111?
A10000
B10001
C11110
D10010
Show Answer & Explanation

Correct Answer: A - 10000

1111 + 1 = 10000 in binary, as the carry propagates through all positions.

Q47.
Which number system is directly used by computers for internal processing?
ADecimal
BOctal
CBinary
DHexadecimal
Show Answer & Explanation

Correct Answer: C - Binary

Computers use the binary number system internally, as digital circuits operate with two states (0 and 1).

Q48.
What is the 9's complement of decimal number 346?
A653
B654
C654
D633
Show Answer & Explanation

Correct Answer: A - 653

9's complement: subtract each digit from 9. 9-3=6, 9-4=5, 9-6=3. Result: 653.

Q49.
Convert decimal 0.625 to binary:
A0.100
B0.110
C0.011
D0.101
Show Answer & Explanation

Correct Answer: D - 0.101

0.625×2=1.25 (1), 0.25×2=0.5 (0), 0.5×2=1.0 (1). So 0.625 decimal = 0.101 binary.

Q50.
What is the range of signed 8-bit numbers in 2's complement?
A-127 to 127
B-128 to 127
C-128 to 128
D-256 to 255
Show Answer & Explanation

Correct Answer: B - -128 to 127

An 8-bit 2's complement number ranges from -128 (10000000) to +127 (01111111).

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